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000864697 1001_ $$0P:(DE-HGF)0$$aBarbarino, S.$$b0$$eCorresponding author
000864697 245__ $$aTopological Devil’s staircase in atomic two-leg ladders
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000864697 520__ $$aWe show that a hierarchy of topological phases in one dimension—a topological Devil's staircase—can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek–Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized.
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000864697 7001_ $$00000-0002-9222-1913$$aRossini, D.$$b1
000864697 7001_ $$0P:(DE-Juel1)177780$$aRizzi, Matteo$$b2
000864697 7001_ $$0P:(DE-HGF)0$$aFazio, R.$$b3
000864697 7001_ $$0P:(DE-HGF)0$$aSantoro, G. E.$$b4
000864697 7001_ $$0P:(DE-HGF)0$$aDalmonte, M.$$b5
000864697 773__ $$0PERI:(DE-600)1464444-7$$a10.1088/1367-2630/ab0e18$$gVol. 21, no. 4, p. 043048 -$$n4$$p043048 -$$tNew journal of physics$$v21$$x1367-2630$$y2019
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